Well the best suggestion that I can make to you is to get a very small Shop-Vac and then buy the attachment-set that they sell for them. And I'll explain why I'm suggesting this over any "hand-held" vacuum, especially since price is an issue to you.
I have a regular vacuum for my house, a quite expensive Shark with a detachable-canister, hose and attachments, etc. I love it, and I only spent as much money as i did after buying several cheap, almost "disposable" vacuum cleaners and having them last for a year or less and then die. So I bit the bullet and spent I think a little over $400 of the Shark, and that's the "inside, house vacuum" to be used only on my carpeting and hard floors inside. That's it. I don't use it to clean-up the bird's messes at all, except for the stray-seeds/shells/feathers that are on the carpet/floors around the house. I don't use it to clean-up around or under their cages, in their cages, etc. I don't want it to get nasty...
So I first bought a DustBuster, quite an expensive DustBuster that has attachments and all kinds of stuff with it, to use around/inside the bird's cages. Well this didn't work-out at all. First of all, even though it's the most expensive DustBuster they make, it hardly holds much at all and constantly has to be emptied. Secondly, IT DOESN'T HAVE ANY POWER!!! I mean, it's great to use around the baseboards, inside/around kitchen cabinets, and is wonderful for doing around/in/on electronics like the TV's, computers, stereo's, my guitars, amps, pedalboards, etc. But as far as cleaning up seeds, shells, feathers, dried poop, etc., it sucks. And it's the expensive DustBuster that cost well-over $100. So it got demoted to being used alongside the Shark as a house-vacuum.
Then I bought a Shark hand-held vacuum with attachments to use for the bird's room/cages/etc. It was also expensive, but I needed to find something to use for the bird's messes, and in the meantime I had been lugging my enormous ShopVac that I use/keep in my garage and for the car, which works amazingly well, but is too big and heavy to keep lugging up and down from the garage constantly. Well, this handheld Shark thing worked well as far as it's power went, but again it didn't hold much at all and constantly had to be emptied...and I soon realized that this was going to be a major issue with ANY "handheld" vacuum. So I sold the handheld Shark thing on Craigslist and only lost $30 from what I paid for it...
So my best advice to you is to do one of a couple of options:
#1) Buy a cheap, regular vacuum with attachments that is to be dedicated to only being used for the bird-messes, and keep it in the same room as the bird's cages.
#2) Find a used, smaller Canister-Vacuum that you can do the same thing with, dedicate it to only being used for the bird-messes and keep it near or in the same room as the bird's cages.
#3) (WHAT I DID) Buy the smallest version of the ShopVac (it's pretty small and light, but still holds a ton, more than most regular vacuums)...Brand-new you can buy one of these at Walmart for $30, either the actual ShopVac brand, or the other one they sell that seems to be rated just as well as the ShopVac brand is the Stanley-brand version, which is exactly the same size and I believe costs exactly the same as well...The only reason I bought the ShopVac brand one is so that the accessory-set they also sell at Walmart would fit, as their hoses are different diameters...So I spent $30 on this very small ShopVac, with the sucking-power of any Dyson or Shark regular vacuum, and then the mini-attachment-set, which comes with like 7 or 8 different tiny attachments for crevices, edges, etc. for like $15, maybe less, I know it wasn't more than $15 new...And it works great, it's small and light, I have an attachment for anything and everything, it holds a ton and never needs emptied, and most of all, IT IS A WET/DRY VACUUM! So you don't have to worry about anything that you are cleaning, their cages, around the cages, their bowls, etc. I just don't put a bag in it, which allows it to be both a wet/dry vacuum, so i don't have to worry about what I'm sucking up, and then just dump it into a trash-bag whenever it's full. And you can just pop the top off and rinse/wash the inside out to clean it if it gets nasty, and then just pull the filter off the top portion with the vacuum motor, and then wipe it down too, rinse out the filter, wring it out, put it back on, and you're good to go! And it is so small that it fits in the folding closet in my bird-room.
Way better all the way around then any handheld vacuum you're going to buy, especially if you're thinking of buying on-the-cheap, as I can't imagine using a cheap DustBuster or Shark handheld based on how crappy the power and how small the capacity was in the really expensive models. The small ShopVac honestly isn't a whole lot larger than a handheld vacuum would be any way...
